Once your return has been accepted by the IRS, only the IRS has any control. TurboTax does not receive any updates from the IRS.
To track your Federal refund:
https://www.irs.gov/refunds
To track your state refund:
https://ttlc.intuit.com/questions/1899433
On the IRS site you are also offered the use of an app called IRS2Go